**The Quantum Classical Clock**

This clock simulates three quantum classical shift registers. The position of each clock hand corresponds to a single moving 1-bit in one of the three shift registers. In the quantum description the 1-bit is in a superposition of integer positions. This is indicated by the color of each dot (wavefunction phase) and its size (wavefunction magnitude). The integer-position values can be considered discrete samples of a uniformly moving continuous wavefunction with a bandlimited Fourier spectrum, which can be exactly reconstructed from just the integer-position values.

Quantum classical shift registers are described by Norman Margolus in Mechanical Systems that are both Classical and Quantum. Here is an illustration of discrete, continuous, and quantum shift registers clocking at the same rate, with some discussion.

The physics of these devices is interesting because it provides an abstraction of computation at the level of bits that can be analyzed as a classical system or a quantum system. One normally thinks of classical and quantum mechanics as existing on opposite sides of a great divide, each being true under its own set of conditions, and never the two shall meet. However, here they meet, and they must both be true.

The clocks are implemented using javascript running in your browser to draw and animate the images. The "canvas" versions use the html5 <canvas> element. They will, eventually, run on all modern, standards compliant browsers, even smartphones. The "SVG" versions use Structured Vector Graphics and will, eventually, run on all modern, standards compliant browsers, too, but they run on fewer at the moment for no good reason.

The visual design of the clocks is being driven by the software problems of making two different rendering techniques produce the same animated images. This forces the visual design into easily parameterized code. But this does not necessarily produce the most visually interesting designs.

The Quantum Classical Clock is Copyright © 2009 by Roger E Critchlow Jr, Santa Fe, New Mexico, USA. All rights reserved. Permission granted for reproduction for personal or educational use.